The Distance Between Classical and Quantum Systems

In a recent paper, a “distance” function, , was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a “distance”, D, which measures the distance between either pure or impure classical and quantum states. We also compare the new distance formula with the previous formula, when the latter is applicable. To illustrate these distances, we have used 2 × 2 matrix examples and two-dimensional vectors for simplicity and clarity. Several specific examples are calculated.     

Hamilton–Jacobi Quantization of Singular Lagrangians with Linear Velocities

In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton–Jacobi method. The integrablity conditions are considered on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians with linear velocities.     

Stabilizing the intensity of a wave amplified by a beam of particles

The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles as in a free electron laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article, we propose a strategy to stabilize the intensity by re-shaping the macro-particle. This strategy involves the study of the linear stability (using the residue method) of selected periodic orbits of a mean-field model. As parameters of an additional perturbation are varied, bifurcations occur in the system which have drastic effect on the modification of the self-consistent dynamics, and in particular, of the macro-particle. We show how to obtain an appropriate tuning of the parameters which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.     

Improved measurements and analysis of the far-infrared spectrum of methanol-D1 (CH2DOH) arising from trans- (e0) to gauche- (e1 & o1) states

In this work the millimeter-wave (MMW) and far infrared (FIR) absorption spectrum for the asymmetrically deuterated Methanol (CH₂DOH) species measured recently at a temperature of −60 °C with better accuracy and signal/noise (S/N) ratio than known before has been assigned for transitions originating at the lowest lying trans- to gauche-states. The entire spectrum for 50–1200 cm⁻¹ has been re-recorded recently using the Synchrotron Radiation Source coupled with the Bruker Fourier Transform Infrared (FTIR) spectrometer with a resolution of about 0.001 cm⁻¹ or better. Complete spectrum has not been exploited a great deal but it helped to entangle overlapping lines in the present work. This also fills the gap remaining in the usual FTIR in the range 400–500 cm⁻¹. Hence it is expected to help the interacting partner for the Coriolis interaction encountered earlier. The assigned transitions mostly for the axial rotational angular momentum quantum number K + 1 ← K, both for R- and Q-sub bands for wide range of rotational angular momentum quantum number. The MMW spectrum has been recalibrated and assigned for a number of Q-branches. The assignments are confirmed rigorously using closed loop residual technique. The assigned ^rR and ^rQ lines have been analyzed in terms of polynomial expansion parameters. The new assignments are presented for about 750 transitions and a grand atlas of more than 1000 lines has been prepared which will be made available through the open source server at “research gate”. The present work should be useful in the area of astrophysical detection and further understanding of the energy relaxation pathways in the molecule.     

Fractional charges and fractional spins for composite fermions in quantum electrodynamics

By using the Faddeev-Senjanovic path integral quantization method, we quantize the composite fermions in quantum electrodynamics (QED). In the sense of Dirac’s conjecture, we deduce all the constraints and give Dirac’s gauge transformations (DGT). According to that the effective action is invariant under the DGT, we obtain the Noether theorem at the quantum level, which shows the fractional charges for the composite fermions in QED. This result is better than the one deduced from the equations of motion for the statistical potentials, because this result contains both odd and even fractional numbers. Furthermore, we deduce the Noether theorem from the invariance of the effective action under the rotational transformations in 2-dimensional (x, y) plane. The result shows that the composite fermions have fractional spins and fractional statistics. These anomalous properties are given by the constraints for the statistical gauge potential.     

Block （or Hamiltonian） Lie Symmetry of Dispersionless D-Type Drinfeld-Sokolov Hierarchy

In this paper, the dispersionless D-type Drinfeld-Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. These flows form an infinite-dimensional Lie algebra of Block type as well as a Lie algebra of Hamiltonian type.     

Rovibrational dynamics of the RbCs molecule in static electric fields. Classical study

We study the classical dynamics of the RbCs molecule in the presence of a static electric field. Under the Born–Oppenheimer approximation, we perform a rovibrational investigation which includes the interaction of the field with the molecular polarizability. The stability of the equilibrium points and the phase space structure of the system are explored in detail. We find that, for strong electric fields or for energies close to the dissociation threshold, the molecular polarizability causes relevant effects on the system dynamics.     

Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures

We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra. Then its super Hamiltonian structure is furnished by super trace identity. As its reduction, we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.     

Discrete integrable system and its integrable coupling

This paper derives new discrete integrable system based on discrete isospectral problem. It shows that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. Finally, integrable couplings of the obtained system is given by means of semi-direct sums of Lie algebras.     

Hamiltonian structure and gauge symmetries of Poincaré gauge theory

This is a review of the constrained dynamical structure of Poincaré gauge theory which concentrates on the basic canonical and gauge properties of the theory, including the identification of constraints, gauge symmetries and conservation laws. As an interesting example of the general approach, we discuss the teleparallel formulation of general relativity.